Erratum: High-order strongly nonlinear long wave approximation and solitary wave solution (J. Fluid Mech. (20225) 945 ( A15) DOI: 10.1017/jfm.2022.544)

doi:10.1017/jfm.2022.544, Published by Cambridge University Press, 18 July 2022 I have discovered that there was an error in one of the second-order equations (the evolution equation for φ_b) given by (5.12b) in Choi (2022), which will be hereinafter referred to as C22. The correct evolution equation for φ_b is given by(equation presented) (0.1) While the recursive formulas in C22 are correct, a mistake was made when the second-order model was simplified. As a result, the second-order evolution equation for v = φ_bx for one-dimensional waves given by (6.1b) in C22 is also incorrect. The evolution equation should read (equation presented). (0.2) Notice that the coefficient for v_xv_xx on the right-hand side has been changed to 3 from 5 in C22. The numerical results presented in figures 9, 11, and 12 in C22 are recomputed with the corrected second-order system, but the new numerical solutions are found close to the previous solutions as the error was introduced in the high-order dispersive terms of O(β⁴) ≪ 1. Therefore, no new numerical solutions are presented here although they are made available at https://web.njit.edu/~wychoi/pub/Choi22~newfigures.pdf. It should be remarked that the maximum difference between the new and old solutions, for example, for the head-on collision of two-counter propagating solitary waves presented in figure 12 in C22 is found about 3.76 %. Therefore, the discussion about the second-order model in C22 remains valid. In the meantime, the loss of the truncated energy for the second-order model is found 0.179 % at t/(h/g)^1/2 = 200 for the propagation of a single solitary wave presented in figure 9 and 0.198 % at t/(h/g)^1/2 = 20 for the head-on collision of two solitary waves in figure 11, instead of 0.230 % and 0.130 %, respectively, reported in C22.